Mode conversion in wave guides



p 1956 s. P. MORGAN, JR 2,762,981

MODE CONVERSION IN WAVE GUIDES Filed Nov. 10, 1951 2 Sheets-Sheet 1 'INVENTOR S. MORGAN, JR.

A T 70 R/VE p 1956 s. P. MORGAN, JR

MODE CONVERSION IN WAVE GUIDES 2 Sheets-Sheet 2 Filed Nov. 10 1951 INVENTOR S. I? MORGAN, JR. BY

ATTOfE/Z United States Patent "ice MODE CONVERSION IN WAVE GUIDES Samuel P. Morgan, Jr., Morristown, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application November 10, 1951, Serial No. 255,836 4 Claims. (Cl. 333-21) This invention relates to the transmission of electromagnetic wave energy in the microwave frequency range through wave guides. It is concerned primarily with the spurious wave modes that may tend to appear in a wave guide in addition to the desired or operating wave mode, and with the transformation of guided waves from one mode to another.

In the transmission of electromagnetic energy through a hollow conductive pipe or other wave guide it is wellknown that the energy can propagate in one or more transmission modes, or characteristic field configurations, depending on the cross-sectional size and shape of the particular guide and the operating frequency, and that the larger the cross-section of the guide is made the greater is the number of modes in which the energy can propagate at a given operating frequency. Very generally it is desired to confine propagation of the energy to one particular mode, chosen because its propagation characteristics are favorable for the particular application involved. If the desired mode happens to be the so-called dominant mode it is feasible to restrict the cross-sectional dimensions of the guide so that no modes other than the dominant mode can be sustained therein. This expedient is not available, however, if the desired mode is not the dominant mode or if a guide of large cross section is prescribed in order, for example, that advantage may be taken of its relatively low attenuation.

For practical example, it may be desired to transmit circular electric waves of lowest order viz., TEoi, through a long-distance wave guide of circular cross section having a diameter several times the operating wave length. Both the choice of mode and large diameter in this case tend to reduce the attenuation, or power loss, suffered by the waves as they propagate through the guide. In such case, however, the guide can sustain numerous other modes including the transverse magnetic mode TMn and circular electric modes of higher order such as TE02 and TEos, and to the extent that the wave power is actually transmitted in these other modes the power loss is substantially increased and other ill effects may occur.

Progressive changes in the size, shape or direction of a wave guide very generally result in the conversion of power from the principal, or operating mode into one or more subordinate, spurious modes. Bends, elbows and taper sections of guide, for example, tend accordingly to generate additional modes and these will be propagated, if the guide be large enough, and thereby introduce deleterious effects. This tendency is so pronounced that under appropriate conditions a single bend, even though of large radius, may convert all of the wave power supplied to it in one mode into a distinctly diflFerent and unwanted mode.

The present invention has as one of its general objectives the reduction or suppression of unwanted modes in a wave guide. More particular objectives are to effect such reduction or suppression with minimum loss of wave power, over relatively broad frequency bands,

2,762,981 Patented Sept. 11, 1956 and/or without substantial reflection of wave power in the operating mode or other ill effect.

A further and more specific objective of the invention is to facilitate the transmission of wave power through curved sections of wave guide.

The present invention proceeds in part upon the observation that a curved section or other element of a waveguide system that tends to convert wave power from the operating mode to some other mode, may itself have natural modes of wave propagation, that is, modes in which the element will transmit power without any tendency to mode conversion.

In accordance with the invention a mode transducer is incorporated within a wave guide adjacent a curved section or the like to convert wave power from the operating mode in the guide to a natural mode in the curved section or the like, or to convert from the natural mode to the operating mode in the opposite direction of transmission.

In embodiments of the invention to be described in detail hereinafter, a bend or other wave guide element that has a natural propagation mode other than the operating mode, is preceded by a first mode transducer such that the wave power passes through. the element without further mode conversion, and a second mode transducer follows the element to restore the wave power'tothe operating mode. The conversion of wave power from the one mode to the other is effected by a dielectric transducer comprising dielectric material that is disposed within the guide in predetermined relation to the characteristic electric field patterns of the two modes, and that may extend a substantial distance longitudinally through the guide. In accordance with a feature of the invention the transducers may be constructed of a material having a dielectric constant that is only slightly higher, forexample less than ten per cent 'higher and preferably in some cases only of the order of two per cent higher, than the dielectric constant of the medium (air or other gas, e. g.) filling the rest of the guiding structure.

The nature of the present invention and its various objectives, features and advantages will appear more fully on consideration of the embodiments illustrated in the accompanying drawings and hereinafter described.

In the drawings:

Fig. 1 illustrates an embodiment of the invention involving a curved section of wave guide;

Figs. 1A and 1B are cross-sectional views of dielectric mode transducers that may be employed alternatively in the Fig. 1 embodiment;

Figs. 2 and 3 are explanatory diagrams pertaining to Figs. 1A and 1B, respectively; and

Figs. 4 to 8 are diagrams to illustrate an exposition of the principles of mode transducer design.

The present application is in part a continuation of my application Serial No. 226,869 filed May 17, 1951,

the disclosure of which is to be deemed incorporated herein.

Referring now to Fig. l, the specific embodiments of the invention chosen for presentation herein involve the.

transmission of wave power in the circular electric (TEOI) mode through a hollow-pipe guide it} of uniform circular cross section that has an interposed curved section 11 of the same cross section. The TEni mode is applied to the circular wave guide 10 by any suitable TEOI mode generator 14. A typical structure for gen erating the TEOJ. mode is shown in Fig. 9.64 on page 355 of a book entitled Waveguide Transmission, by

George C. Southworth, D. Van Nostrand Co., Inc., New.

York, 1950.

The theory of propagation of TEOI waves through an arcuately curved wave-guide bend has been extensively treated in the literature (see for example, M. Jouget, Cables -et TTansrnissi-on, v. 1, No. 2, July 1947, pp. I33 153, and v. 2, No. 4, October 1948, pp. 257-284) and it is there shown thatwhen such a bend is encountered the applied TEm waves are progressively converted into the TMM mode with aparticular polarization. It is also known that the two modes have exactly the samephase velocity in a straight pipe, a circumstance which leads to close coupling between these two modes in a curved guide. In the bend the conversion into the TM11 mode may be partial or complete, depending on the dimensions, and in fact there may be several complete conversions from one mode to the other in alternation.

A curved wave guide has several natural modes, that is, modes which it will propagate without mode conversion. Certain of these modes .are so-called mixed modes, i. e., combinations containing both transverse electric and transverse magnetic components. Two of these natural modes in a curved guide of circular cross section are known as the TEoi+TMn" mode and the TEo1T M11" mode, each comprising a TEoi component and an equal TM11 component. Both of the TM11 components have a particular orientation relative to the plane of the bend, as illustrated in Fig. 2, and each has a particular .phase relation with its associated TEm component. Those phase relations are not the same .as the phase relation between an applied TEur wave and the TM11 mode produced in the bend by mode conversion.

A third natural mode of the bend his the TMn' mode. It has only a TMii component and it is oriented in the bend in the manner shown in Fig. 3. The polarization of this component, it will be observed, is displaced ninety degrees from that of the TM11" component of the TEoriTMn" modes.

Referring again to Fig. 1, the straight section ofguide between the source of TEoi waves and the bend 11 contains a mode transducer 12 that is adapted to convert the TEoi waves applied to it into one of the abovedescribed natural modes of the bend. Similarly, in the straight section of guide 10 at the other end of the bend there is incorporated a mode transducer .13 that converts the waves issuing from the bend back into the TE01 operating mode. Both of the transducers are reciprocal in their operation and so may have the same construction.

With regard to the space, if any, between the transducers 12 and 13 and the bend 11, it is to be noted that the natural modes of the bend are also natural modes of the straight guide and that, accordingly, there is no mode distortion in these spaces. The transducers should be disposed adjacent the bend, however, for in a long section of straight guide the TM11 component would have a substantially higher attenuation than the TED]. mode. This arrangement also reduces or eliminates any shift in the polarization of mode components that might arise from imperfect circularity of the guide.

The transducers 12 and 13 in Fig. 1 are dielectric mode transducers of the general type treated in my copending application, supra. Suitable specific structures in accordance with the present invention will be set forth hereinafter. The underlying principles may be better understood, however, from a consideration of the following exposition of related structures disclosed and claimed in the aforesaid application.

Referring now to Fig. 4, there is represented diagrammatically at A the electric .field configuration characteristic of the TEoi mode in a circular guide, while B and C are applicable similarly to the TEoz and TEos modes, respectively. In each case the electricfield is symmetrical about the axis and varies in intensity from center-to periphery of the guide in known manner. In the 'TEoi mode the phase is the same from axis to periphery, as indicated by the arrows. In the TEoz mode the phase is the same from the axis out to a cylindrical node of radius p, equal to 0.546 a where a is the radius of the guide, and the opposite relative phase prevails in the tubular zone extending from that node to the periphery. In the TEos mode there are three such cophasal zones, viz., a central zone extending from the axis to a node of radius p equal to 0.377 a; an outer cophasal zone, of the same phase as the first, extending from a node of radius p equal to 0.690 a to the periphery; and a third cophasal zone, opposite in phase relative to the other two and lying between them.

I'have found that if in a wave guide carrying the TEo1 mode, as in A, dielectric material be placed in one or the other of the two cophasal zones of B, some of the energy ofthe operating mode will .be converted into the TEaz mode, and further that any tendency to generate non-circular modes can be reduced by disposing the dielectric material symmetrically about the axis of the guide, i. e., in the form of a (solid or hollow) cylinder coaxial with the guide. The maximum generation of the TEoz mode occurs if the dielectric just fills the inner cophasal zone, i. e., the space from the axis of the guide to the first node of .the electric field, as illustrated in Fig. 5, or if it just fills theouter cophasal zone, i. e., the space between the first node and the metal shell 10 of the guide, as illustrated in Fig. 6. The two dielectric elements 21, 22, of Figs. 5 and 6, assumin them to .be of the same length, are complementary in that the TE02 waves theygenerate are equal in amplitude and opposite in phase. This can be readily appreciated on observing that the two (generalized) cylinders together would form a solid dielectric plug filling the guide and that such a plug would generate no modes other than TE01 .under the influence of a pure TEDl wave.

Similarly, the most efiicient disposition of dielectric material for the generation of the TEos mode is in the form of a hollow cylinder or tube 13. just filling theintermediate cophasal zone, as illustrated in Fig. 7, or in the form .of a pair of cylinders 24, 25, one just filling the inner cophasal zone and the other a tube just filling the outer one, as illustrated in Fig. 8. The dielectric structures in Figs. '7 and 8, respectively, are complementary to each other with respect to the generation of the TE03 mode or any other mode.

The same principles are applicable to other guide shapes and modes generally, excepting only unusual cases where the electric field vector of the mode to be generated is perpendicular at every point to the electric field vector of the operating mode. The cophasal zones can be identified readily by-superposing the electric field .diagrams of the operating mode and the mode to be derived, and marking the boundaries between regions in which the electric vector of the operating mode (or, more generally, the projection thereof) coincides-in direction and phase with the electric vector of the other mode, and similar regions in which the relative phases are reversed. Diagram D in Fig. 4, for example, illustrates the dominant'mode TEm in :a guide of rectangular cross section, while .at E are illustrated the TEzo mode in the same guide, the two equal cophasal zones "that appear, and the disposition of dielectric material in one of thetwo cophasal .zones ,for maximum conversion of wave power from .the first of these modes to the second. Forrnaximum .generation of the 'TEKo mode the dielectricmaterial may fill the central one of the three equal cophasal zones shown at F in 'Fig. 4 or it may fill both of the adjoining; zones which constitute a cophasal region of the opposite relative *phas The specific dimensions that-havebeen assigned to the dielectric mode transducers of Figs. 5 to 8 are, as indicated, those that, with ai given dielectric material, yield maximum generation of a prescribed secondary *mode for a given over-all length of transducer, and it has been pointed out that complementary transducers are equallyeffective. In various practical applications of the invention, however, other iactors than maximum generation are significant or even controlling and they maydictate the choice of one transducer over another or call for modification of the dimensions given. One such factor is ease of fabrication, or mechanical support for the dielectric members. The tubular dielectric member in Fig. 6, e. g., is self-supporting within the guide; the complementary dielectric member in Fig. 5 is not. The latter can be supported by a contiguous dielectric plug; or if the transducer is interposed in a wave guide that is filled with solid dielectric material it can be supported by a surrounding tube of that same material. In some cases another factor, the total volume of dielectric material required, may favor the choice of one design instead of another.

Another factor in the design of a dielectric mode transducer that may be significant in certain circumstances is the tendency of the transducer to generate modes other than the prescribed secondary mode or modes. The transducers of Figs. 5 and 6, for example, generate the T1503 mode in some slight degree, because the dielectric fills one of the like-phased cophasal zones of this mode (Fig. 4C), and thus tends to generate the T1303 mode but it does not extend quite the proper distance into the adjacent oppositely-phased zone to effect cancellation. A secondary mode so generated will be suppressed, however, if its cut-off frequency is greater than the operating frequency, i. e., if the guide be of SlliTlClGDtlY small size. If not so suppressed it may happen to be of such amplitude and phase as to oppose and reduce a wave component of the same mode originating elsewhere in the guide. The generation of any particular secondary mode can be obviated, in any event, by so disposing the dielectric material of the mode transducer that any dielectric material in one cophasal zone of that mode is balanced by dielectric material in a co phasal zone of the opposite phase. Applying this principle to the transducers of Figs. 5 and 6, for example, it will be found that if the indicated radius is changed from 0.546 a to 0.529 a none of the TE03 mode will be generated.

Still another factor is the relation between the dielectric constants of the several dielectric media, that is, the two dielectric media in the transducer section and the dielectric medium in the adjoining sections of guide. The more closely the average or effective dielectric constant in the transducer section approximates the dielectric constant in the adjoining sections, the more completely is the transducer reflectionless. The more nearly alike the dielectric constants of the media in the transducer section the lower are internal reflections and reflection losses in composite transducers. The greater, too, is the length of transducer required, and in some cases this in itself is advantageous. It will be understood, then, that as a special case the adjoining guide may contain a solid dielectric medium and the transducer may comprise a first dielectric of the same or lower dielectric constant and a second dielectric (a gas, for example) of still lower dielectric constant.

Consistently with the foregoing principles of mode transducer design, and as illustrated in Figs. 2 and 3, conversion between TEoi and TM11 modes in a round guide can be eifected by a dielectric obstacle placed on one side or the other of the diametral plane of symmetry of the TM11 mode. The maximum rate of conversion is obtained if the obstacle is of semi-circular cross section, as in Fig. 3 where it completely fills one of the cophasal zones.

[f in Fig. 1 the natural mode selected for propagation through the bend 11 is either the TE01+TM11 mode or the TEoiTM1r mode the transducer 12 is required to translate half of the TEOI wave power supplied to it into a TNn component that is oriented with its diametral plane of symmetry perpendicular to the plane of the bend, as indicated in Fig. 2, and that has the proper phase relative to the TEM component. For this purpose the transducer may take the specific form illustrated in Figs. 1A

arid 2 where the cross section of the dielectric member appears as sector of half-angle or disposed with the bisector in the plane of the bend and directed toward or away from the center of curvature depending on which of the two mentioned natural modes is chosen. If the TEor-l-TMu" mode be chosen, the dielectric is disposed toward the outside of the bend, that is, with the bisector directed away from the center of curvature of the bend. The length l and the half-angle on of the transducer aifect both the amplitude and relative phase of the generated TMu component, and they may be calculated as follows.

The half-angle a is a function only of the ratio v= where is the free wavelength corresponding to the operating frequency and A =2ira/3.8317 is the cutoff Wavelength for the TE01 and TM11 modes in a straight guide of the given radius a. a In radians satisfies the equation where O u 1r.

With or so determined, the required length l of the mode transducer is given by 0.6823(e,1) sin or (2) where E is the relative dielectric constant of the transducer material, and it is assumed that e does not differ much from unity.

The second mode transducer, 13, may be of exactly the same construction as transducer 12 and disposed in the same way relative to the bend.

A disadvantage of the embodiment last described is that Equation 1 yields a real value of or only for values of u ranging from 0.85 to unity. That is, the operating frequency must be closer to the cut-off frequency than will be found desirable in many instances in practice.

The foregoing disadvantage is avoided and various advantages are secured in an alternative embodiment of the invention that makes use of another of the natural modes of Wave propagation in the bend, viz., the TM11' mode. In this embodiment the dielectric obstacle comprising each transducer is semicircular in cross section and disposed with its diametral surface in the plane of the bend, as illustrated in Figs. 13 and 3. The length l of the obstacle is that required for the complete conversion of TEOl waves into TM11 waves, and this may be easily determined empirically or by calculation as follows:

where is the free-space wavelength corresponding to the operating frequency.

In a specific illustrative example, A is 1.25 centimeters, a is 2.54 centimeters, v is calculated to be 0.300, e is 1.0200, and l is centimeters.

In the empirical determination of the length I one need only assemble semicircular plates of the dielectric ma- 'terial in the guide, one after another, until test shows no residue of power in the TEor mode.

To hold the dielectric transducer members in place various expedients may be employed. For example, discs of the same dielectric material may be attached, integrally or otherwise, to the ends of the members, as shown in Fig. 1, and cement may be used to prevent longitudinal or rotational displacement. The transducers described do not tend to generate modes other than TM11 in any substantial degree since all modes other than TM11 differ in phase velocity from the TE01 mode. Hence over a distance of many wavelengths these other modes will phase in and out so often that the net power transfer will be small.

Numerous other embodiments Within the spirit and scope of the invention, in addition to those specifically described herein, will be obvious to those skilleduin the art.

What is claimed is:

1. In combination, an elongated substantially circular wave guide having two straight sections and a curving bend section interconnecting said straight sections, means for generating electromagnetic waves of the TEM mode coupled to one of said straight sections of wave guide, and means for interconverting electromagnetic wave energy between the T1301 mode in said straight sections and a natural mode of said curved section, said means including two elongated substantially sectorshaped'dielectric obstacles each of which have a relative dielectric constant greater than 1.0 but less than 1.1 located respectively in said two straight sections of wave guide adjacent said curved section.

2. In combination, an elongated substantially circular wave guide having two straight sections and a curving bend section interconnecting said straight sections, means for generating electromagnetic Waves of the TEoi mode coupled to one of said straight sections of wave guide, and means for interconverting electromagnetic wave energy between the TEo1 mode in said straight sections and a natural mode of said curved section, said means including two elongated substantially sector-shaped dielectric obstacles each of which has a relative dielectric constant greater than 1.0 but less than 1.1 located respectively in said two straight sections of wave guide on one side of a diametral plane parallel to the plane of the curved section of wave guide.

3. In combination, an elongated substantially circular wave guide having two straight sections and a curving bend section interconnecting said straight sections, means for generating electromagnetic waves of the TEM mode coupledto one of said straight sections of wave ,guide, and means for interconverting electromagnetic wave energy between the TEOI mode in said straight-sections'and a natural mode of said curved section, said meansin'cluding two elongated substantially sector-shaped dielectric obstacles each of which has a relative dielectric constant greater than 1.0 but less than 1.1 located respectively in said two straight sections of waveguide adjacent said curved section, aid dielectric obstacles being symmetrically oriented with respect to a diametral plane parallel to .the .planexof the curved section of wave guide and passing through the center thereof.

4. In combination, a microwave frequencywave. guide transmission line of circular cross-section, said line comprising at least two straight portions interconnected by acurved portion, said line being adapted to transmit wave energy of the TEM mode, means for eliminating the degeneration of the TEm mode wave energy into unwanted modes of wave energy while traversing a curved portion of said wave guide transmission line, said means comprising a pair of mode converters, one of said c0n-' verters being situated in said wave guide immediately adjacenteach end of said curved portion, respectively, said mode converters each comprising elongated substantially sector-shaped dielectric obstacles, said mode converters converting 'TEoi mode wave energy into TMll mode wave energy and TMn mode wave energy into TEm mode wave energy, respectively, whereby TEOI modewave energy entering said curved portion of wave guide is converted into TMii wave energy and TMn wave energy emerging from said curved portion is converted 'into TEoi mode wave energy, and no degeneration of said TEOI mode wave energy into unwanted modes of wave-energy occurs.

References Cited in the file of this patent UNITED STATES PATENTS 2,129,669 

